Many systems of fundamental or technological importance exist as polydisperse mixtures of heterogeneous components. The elucidation of the characteristic properties of the individual components in such mixtures is a crucial problem in fields ranging from analytical chemistry to biophysics.
Particle size measurement in heterogeneous mixtures of particles is a common problem in fields extending from pharmaceuticals, where size measurements diagnose the solubility and purity of therapeutic agents, to paints, inks and coatings, for all of which the size of nano and microscale components has to be controlled and monitored closely to ensure desired functionality.
A field where the sizes of nanoscale components are particularly crucial and of great defining importance is that of protein association and self-assembly; the vast majority of proteins fulfil their biological function not as monomeric species but as part of larger functional complexes; if the assembly of proteins in to such complexes does not occur in the desired manner and aberrant species are formed, this abnormal assembly frequently leads to malfunction and disease. Current biophysical techniques commonly adopted to measure the size of polypeptides perform best for homogeneous preparations of purified components, whereas the quantitative study of heterogeneous mixtures characteristic of many biological systems remains challenging.
Current microfluidic diffusion based sizing techniques [1] have been primarily directed at finding the size of a single species in a homogeneous solution [5] or measuring the interaction between two discrete species, typically using fluorescently labelled species [8, 7, 3, 11, 12, 19]. Techniques which do not require fluorescent labelling of the sample have also been reported [4].
For example, Yager et al. [11] describe a T-sensor for use in the optical measurement of transverse molecular diffusion in a microchannel. The T-sensor has two input ports through which an analyte-containing fluid and a buffer fluid are provided. The two streams of fluid are brought into contact at the T-junction and are permitted to flow side by side along a detection channel. The analyte diffuses from the analyte fluid into the buffer fluid as the flows proceed along the channel. The authors use several fluorescently-labelled proteins as test analytes, and the diffusion of these proteins is detected by fluorescence microscopy at a measurement location downstream of the junction. The methods described are focussed on the analysis of monodisperse analyte solutions.
Yager et al. note that diffusion coefficient values calculated from the recorded experimental diffusion data include an error relating to an assumption in the calculations that the fluids have a fully developed velocity profile throughout the detection channel. This assumption is not correct, as the authors explain. In fact, the velocity of the fluids is observed to accelerate along the channel from a stagnation point where the fluids are first brought into contact (a zero flow region at the junction) to the fully developed velocity at a point further downstream, in order to compensate for this region of slower fluid flow, the authors describe computational methods to explain and quantify the flow development. By the authors own admission, the solutions to the computational calculations are coarse, are slow to calculate (ca. 1 day of computational time), and can only give an idea as to the magnitude of the diffusion effects in the so-called flow development region, it follows that the diffusion coefficients calculated from the recorded data do not adequately compensate for the stagnation of fluids at the T-junction.
US 2006/263903 describes the use of a plus (+) shaped microchannel network to determine the molecular weight and the diffusivity of a sample solute. Here, a single analyte fluid flow is brought into contact with a single blank fluid flow at a cross point. The flows are subsequently separated, with each flow leaving the contact zone in a separate exit channel. The amount of analyte that has diffused into the blank fluid flow in the contact zone is determined for a range of different analyte and blank fluid flow rates. The diffusivity and molecular weight of the analyte is determined by comparison of the recorded diffusion profiles with a diffusivity profile data set generated from the diffusion of standard molecules. The methods described are focussed on the analysis of monodisperse analyte solutions.
Also known in the art are alternative fluidic methods for the determination of diffusion characteristics based on the Taylor dispersion of a species in a fluid channel. For example, US 2011/264380 describes methods for determining the hydrodynamic radius of a polydisperse species. The species to be analysed is mixed with a monodisperse standard. The resulting mixture is added to a carrier fluid flowing along a capillary tube and the Taylor profile of the mixture as it exits the capillary is recorded.
As US 2011/264380 notes, Taylor dispersion methods are not suitable for use with polydisperse mixtures, as the results obtained are simply an average signal that reflects the global properties of the mixture rather than the individual contributions of each component in the mixture. US 2011/264380 partially addresses this point by using an internal standard within a polydisperse sample, which standard provides a known contribution to the average signal. For example, where a polydisperse polymer product is analysed, an internal standard which is a monomer precursor may be present. The contribution of the polydisperse species to the overall signal may then be deduced, and the mean hydrodynamic radius of the polydisperse species may be determined. Nevertheless, this method can only provide the mean hydrodynamic radius for a polydisperse mixture. Moreover, methods based around Taylor dispersion require a time resolved measurement of diffusion, which typically has a lower sensitivity compared to the steady state methods described by Yager et al. [11].
The present inventors have developed methods of analysis that take into account the problems of analysing component diffusion in flow channels.